Question

Let X and Y be two continuous random variables with joint probability density function f(x,y) =...

Let X and Y be two continuous random variables with joint probability density function

f(x,y) =

6x 0<y<1, 0<x<y,

0 otherwise.

a) Find the marginal density of Y .

b) Are X and Y independent?

c) Find the conditional density of X given Y = 1 /2

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X and Y be two continuous random variables with joint probability density function f(x,y) =...
Let X and Y be two continuous random variables with joint probability density function f(x,y) = xe^−x(y+1), 0 , 0< x < ∞,0 < y < ∞ otherwise (a) Are X and Y independent or not? Why? (b) Find the conditional density function of Y given X = 1.(
For continuous random variables X and Y with joint probability density function. f(x,y) = xe−(x+y) when...
For continuous random variables X and Y with joint probability density function. f(x,y) = xe−(x+y) when x > 0 and y > 0 f(x,y) = 0 otherwise a. Find the conditional density F xly (xly) b. Find the marginal probability density function fX (x) c. Find the marginal probability density function fY (y). d. Explain if X and Y are independent
The joint probability density function of two random variables X and Y is f(x, y) =...
The joint probability density function of two random variables X and Y is f(x, y) = 4xy for 0 < x < 1, 0 < y < 1, and f(x, y) = 0 elsewhere. (i) Find the marginal densities of X and Y . (ii) Find the conditional density of X given Y = y. (iii) Are X and Y independent random variables? (iv) Find E[X], V (X) and covariance between X and Y .
Let X and Y be jointly continuous random variables with joint density function f(x, y) =...
Let X and Y be jointly continuous random variables with joint density function f(x, y) = c(y^2 − x^2 )e^(−2y) , −y ≤ x ≤ y, 0 < y < ∞. (a) Find c so that f is a density function. (b) Find the marginal densities of X and Y . (c) Find the expected value of X
Let X and Y be two continuous random variables with joint probability density function ?(?, ?)...
Let X and Y be two continuous random variables with joint probability density function ?(?, ?) = { ? 2 + ?? 3 0 ≤ ? ≤ 1, 0 ≤ ? ≤ 2 0 ??ℎ?????? Find ?(? + ? ≥ 1). Sketch the surface in the ? − ? plane.
X and Y are continuous random variables. Their joint probability distribution function is : f(x,y) =...
X and Y are continuous random variables. Their joint probability distribution function is : f(x,y) = 1/5(y+2) , 0 < y < 1, y-1 < x < y +1 = 0, otherwise a) Find marginal density of Y, fy(y) b) Calculate E[X | Y = 0]
Suppose that the joint probability density function of the random variables X and Y is f(x,...
Suppose that the joint probability density function of the random variables X and Y is f(x, y) = 8 >< >: x + cy^2 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 0 otherwise. (a) Sketch the region of non-zero probability density and show that c = 3/ 2 . (b) Find P(X + Y < 1), P(X + Y = 1) and P(X + Y > 1). (c) Compute the marginal density function of X and Y...
The joint probability density function of two random variables (X and Y) is given by fX,Y...
The joint probability density function of two random variables (X and Y) is given by fX,Y (x, y) = ( C √y (y ^(α+1)) exp {( − y(2β+x ^2 ) )/2 } , x ∈ (−∞,∞), y ∈ [0,∞), 0 otherwise. (a) Find C. (b) Find the marginal density of Y . What type of distribution does Y follow? (c) Find the conditional density of X | Y . What type of distribution is this?
X and Y are continuous random variables. Their joint probability density function is given as f(x,y)...
X and Y are continuous random variables. Their joint probability density function is given as f(x,y) = 1/5 (y+2) for 0<y<1 and y-1<x<y+1. Calculate the conditional expectation E(x/y=0). Please show all the work and explain if the answer will be a number or just y in a given range.
Let X and Y be a random variables with the joint probability density function fX,Y (x,...
Let X and Y be a random variables with the joint probability density function fX,Y (x, y) = { cx2y, 0 < x2 < y < x for x > 0 0, otherwise }. compute the marginal probability density functions fX(x) and fY (y). Are the random variables X and Y independent?.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT